Posted: 3/22/2012 5:07:19 AM EDT
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Arfcom i need your help.
Im doing a maths presentation on the mathematics of projectiles. Any relevent resources on ballistics (direct and indirect fire) would be most welcome. |
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Arfcom i need your help. Im doing a maths presentation on the mathemathics of projectiles. Any relevent resources on ballistics (direct and indirect fire) would be most welcome. Coriolis Effect and Spin Drift are two of the more complex things that you could model mathematically, just for the heck of it. Someone is always talking about these phenomena, but 99.9% of shooters will never notice the effect of either. |
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Start here... http://en.wikipedia.org/wiki/Ballistics Do some research in fluid dynamics, look of the Coefficients of friction for various rounds... The answers you seek are all over the InterWebz... |
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Google "external ballistics" Also look up the references from the wikipedia article of the same title. You may want to check your spelling of mathematics, unless that's a British English thing... Not British English i just cant spell for toffee. Good advice guys, thanks. |
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US Army FM 6-40 Manual Cannon Gunnery. There's a whole mess at the beginning on ballistics.
I believe it's Chapter 3 (don't have FM in front of me). You can read about internal, transitional, exterior, and terminal ballistics. Plus (if you're really feeling snazzy) the 14 factors affecting muzzle velocity. If that doesn't satisfy your appetite, there's one or two other books I could recommend when I get home and look at my library If you're trying to find the FM, google APD Army Publishing Directorate |
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There is also this,
http://www.nennstiel-ruprecht.de/bullfly/index.htm Sierra has a pretty good resource that used to be online as well. It was the same as what they had in the back of their reloading manuals on ballistics. |
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Be sure to calculate for this: http://i59.photobucket.com/albums/g302/impactco/partialtarget.jpg That looks like a Google Earth view of a fishing tournament... |
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Be sure to calculate for this: http://i59.photobucket.com/albums/g302/impactco/partialtarget.jpg That looks like a Google Earth view of a fishing tournament... Took a minute to realize it was not that. Keyholes, was a smooth bore used? 
TXL |
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Be sure to calculate for this: http://i59.photobucket.com/albums/g302/impactco/partialtarget.jpg That looks like a Google Earth view of a fishing tournament... Took a minute to realize it was not that. Keyholes, was a smooth bore used?
TXL It probably was a 5.45 AK from Century with a 5.56 bbl. Posted Via AR15.Com Mobile |
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Be sure to calculate for this: http://i59.photobucket.com/albums/g302/impactco/partialtarget.jpg That looks like a Google Earth view of a fishing tournament... Took a minute to realize it was not that. Keyholes, was a smooth bore used?
TXL I see two that stabilized... |
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Arfcom i need your help. Im doing a maths presentation on the mathematics of projectiles. Any relevent resources on ballistics (direct and indirect fire) would be most welcome. Just how much "maths" have you done? Basic maths for engineering at the college level. I have to a 20 minute presentation on the topic and im supposed to learn the stuff myself. So unless its crazy level maths i should be fine. Hopefully. |
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(initial volocity)^2 x sin of 2 Theta = 32 ( distance in feet)
X (distance) = (initial volocity) x time x cos Theta Y( height) =( -16xtime)^2 + (initial volocity) x time x sin Theta Trying to get these formulas to look right on an iPad is not easy but these should give you basic calculations for projectiles ignoring air resistance. Initial volocity is abbreviated as Vo, Time as t... Just say its magnets 
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(initial volocity)^2 x sin of 2 Theta = 32 ( distance in feet) X (distance) = (initial volocity) x time x cos Theta Y( height) =( -16xtime)^2 + (initial volocity) x time x sin Theta Trying to get these formulas to look right on an iPad is not easy but these should give you basic calculations for projectiles ignoring air resistance. Initial volocity is abbreviated as Vo, Time as t... Just say its magnets Unfortunately for us down here in the atmosphere, we DO have to compensate for drag...
(But I much prefer being able to breath...) |
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Not sure how useful it'll be, but this site is kinda awesome:
http://ballisticsbytheinch.com/ |
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(initial volocity)^2 x sin of 2 Theta = 32 ( distance in feet) X (distance) = (initial volocity) x time x cos Theta Y( height) =( -16xtime)^2 + (initial volocity) x time x sin Theta Trying to get these formulas to look right on an iPad is not easy but these should give you basic calculations for projectiles ignoring air resistance. Initial volocity is abbreviated as Vo, Time as t... Just say its magnets Unfortunately for us down here in the atmosphere, we DO have to compensate for drag...
(But I much prefer being able to breath...) It was from my trig class pretty fun but didn't take into account a lot of things... "1) a soldier is accused of breaking a window at 3300 feet away during target practice. If the muzzle velocity for a M-16 is 325 ft/sec, then at what angle would it have to be aimed for the bullet to travel 3300 feet?" It's nice to have math problems that mention guns in a class room with out dogs getting shot and the swat team called, but to consider all variables of a projectile is going to be some serious calculations by hand with a calculus background and understanding of physics and fluids... I'm not there yet (pre-cal). |
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My recommendation is focus on a single aspect, such as the effect of bullet shape on drag (and ballistic coefficient), with some examples of the effect on trajectory at a fixed muzzle velocity. The overall field is too large to distill into a few charts, you'll have to stick with some fundamental characteristics.
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| I'm thinking back to my high school physics class. Doesn't the bullet drop at the rate of gravity (9.82m/s^2)? So if you fired a bullet parallel to the horizon and dropped a bullet by hand at the same time, they would both it the ground at the same time? Where the shot bullet hits the ground can be determined by solving for time on the drop, then using velocity to determine how far it would go, I think? This would ignore drag and slowdown, but is it a close approximate? |
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I'm thinking back to my high school physics class. Doesn't the bullet drop at the rate of gravity (9.82m/s^2)? So if you fired a bullet parallel to the horizon and dropped a bullet by hand at the same time, they would both it the ground at the same time? Where the shot bullet hits the ground can be determined by solving for time on the drop, then using velocity to determine how far it would go, I think? This would ignore drag and slowdown, but is it a close approximate? That's what's going on in the equations above. It's splitting the velocity into x-axis and y-axis components using trig. Time will be the constant between the two. The time it takes to go up and down will allow you to figure out how far it goes horizonatlly. |
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The wiki page on ballistics is pretty good.
Are you going to include the following: -air resistance -Spin drift -Correolis (or however you spell it) The basic mathmatics of 2 dimensional motion in a gravitational field are otherwise pretty simple. There are plenty of models available for shooters online to give you how much of a variety there is between the "right" answers. |
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Spin drift is super easy.
Grab Bernouli's equation and run it up with the Magnus Effect (just hit Wiki, it's correct). You'll want to use a relatively large projectile frequently shot at long ranges - 50BMG is perfect. For a right hand twist, the bullet will drift left when moving upwards, and it will drift right when falling. Calculate the effect for still air. For cross-wind, the bullet will drop in a left-to-right wind, and rise in a right-to-left wind. Assume there's no vertical component to the wind. Merge your results and present a single tool to compensate for spin drift at long range. Yes, ballistics software already exists that does it. But then, every bit of math you could learn at this point has already been done. You're just doing the research. |
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I'm thinking back to my high school physics class. Doesn't the bullet drop at the rate of gravity (9.82m/s^2)? So if you fired a bullet parallel to the horizon and dropped a bullet by hand at the same time, they would both it the ground at the same time? Where the shot bullet hits the ground can be determined by solving for time on the drop, then using velocity to determine how far it would go, I think? This would ignore drag and slowdown, but is it a close approximate? That's what's going on in the equations above. It's splitting the velocity into x-axis and y-axis components using trig. Time will be the constant between the two. The time it takes to go up and down will allow you to figure out how far it goes horizonatlly. I think that's exactly how my physics teacher explained it. Wish I remembered more 
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Be sure to calculate for this: http://i59.photobucket.com/albums/g302/impactco/partialtarget.jpg Ruger Mini-14?
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